Calculator Inputs
Results appear above this form after submission. Use the example button for a ready-made test case.
Example Data Table
| Topology | Inductance | Capacitance | Resistance | Resonance Frequency | Q Factor | Bandwidth |
|---|---|---|---|---|---|---|
| Series | 10 mH | 100 nF | 12 Ω | 5032.92 Hz | 26.35 | 190.99 Hz |
| Parallel | 5 mH | 200 nF | 2.5 kΩ | 5032.92 Hz | 15.81 | 318.31 Hz |
Formula Used
Core resonance equations
Resonance frequency: f₀ = 1 / (2π√LC)
Angular resonance: ω₀ = 1 / √LC
Period: T = 1 / f₀
Reactances: Xₗ = 2πfL and Xc = 1 / (2πfC)
Series RLC relationships
Quality factor: Q = ω₀L / R = 1 / (ω₀CR)
Bandwidth: BW = f₀ / Q = R / (2πL)
Half-power condition: |Xₗ - Xc| = R
Parallel RLC relationships
Quality factor: Q = R√(C / L)
Bandwidth: BW = f₀ / Q = 1 / (2πRC)
Half-power condition: |ωC - 1 / (ωL)| = 1 / R
This calculator uses idealized closed-form equations. It is excellent for design checks, teaching, and first-pass sizing, but measured results can shift because of tolerance, parasitics, and frequency-dependent losses.
How to Use This Calculator
Enter the inductor value and choose its unit.
Enter the capacitor value and select the correct unit.
Provide resistance and choose series or parallel mode.
Add supply voltage if you want current estimates.
Set sweep limits to control the Plotly resonance curve.
Press Calculate Resonance to show results above the form.
Use the CSV or PDF buttons to export outputs.
Check the example table and formulas for validation support.
Frequently Asked Questions
1) What does this calculator compute?
It calculates resonance frequency, angular resonance, period, resonant reactance, quality factor, bandwidth, cutoff frequencies, impedance at resonance, and current estimates. It also plots how impedance and current change around resonance for the selected circuit type.
2) Why does resistance not appear in the basic resonance formula?
The ideal resonance point mainly depends on energy exchange between L and C. Resistance affects sharpness, bandwidth, and current level, but the simple closed-form resonance frequency still comes from the LC pair in standard idealized analysis.
3) Why are the Q formulas different for series and parallel circuits?
Series and parallel networks store and dissipate energy differently. In series mode, resistance directly limits loop current. In parallel mode, resistance controls input conductance, so the algebra changes even though both describe resonance sharpness.
4) Which units can I use?
You can enter inductance in H, mH, uH, or nH. Capacitance supports F, mF, uF, nF, and pF. Resistance supports ohms, kilo-ohms, and mega-ohms. Voltage supports volts and millivolts.
5) Why does the resonance curve look broad sometimes?
A broad curve means lower Q and larger bandwidth. That usually happens when resistance is relatively high in series mode, or relatively low in parallel mode. More damping spreads the response over a wider frequency range.
6) Can I use zero resistance?
In series mode, zero resistance represents an ideal lossless case. The calculator flags Q and bandwidth as ideal or undefined. In parallel mode, zero resistance would short the input, so the model requires a positive value.
7) What are cutoff frequencies f1 and f2?
They are the two half-power points around resonance. Between them lies the bandwidth. These frequencies are useful for filter work, tuning studies, and checking how selective the resonant circuit will be in practice.
8) When can real measurements differ from this result?
Measured values can shift because components have tolerance, coil resistance, core losses, lead inductance, stray capacitance, temperature drift, and instrument loading. At higher frequencies, parasitics become more important and can noticeably move the true resonant peak.